diff options
Diffstat (limited to 'theories/Numbers/Cyclic/DoubleCyclic/DoubleBase.v')
| -rw-r--r-- | theories/Numbers/Cyclic/DoubleCyclic/DoubleBase.v | 21 |
1 files changed, 8 insertions, 13 deletions
diff --git a/theories/Numbers/Cyclic/DoubleCyclic/DoubleBase.v b/theories/Numbers/Cyclic/DoubleCyclic/DoubleBase.v index af113da2b4..d92e818ffa 100644 --- a/theories/Numbers/Cyclic/DoubleCyclic/DoubleBase.v +++ b/theories/Numbers/Cyclic/DoubleCyclic/DoubleBase.v @@ -10,12 +10,14 @@ Set Implicit Arguments. -Require Import ZArith. +Require Import ZArith Ndigits. Require Import BigNumPrelude. Require Import DoubleType. Local Open Scope Z_scope. +Local Infix "<<" := Pshiftl_nat (at level 30). + Section DoubleBase. Variable w : Type. Variable w_0 : w. @@ -68,13 +70,7 @@ Section DoubleBase. end end. - Fixpoint double_digits (n:nat) : positive := - match n with - | O => w_digits - | S n => xO (double_digits n) - end. - - Definition double_wB n := base (double_digits n). + Definition double_wB n := base (w_digits << n). Fixpoint double_to_Z (n:nat) : word w n -> Z := match n return word w n -> Z with @@ -291,11 +287,10 @@ Section DoubleBase. Lemma double_wB_wwB : forall n, double_wB n * double_wB n = double_wB (S n). Proof. intros n;unfold double_wB;simpl. - unfold base;rewrite (Zpos_xO (double_digits n)). - replace (2 * Zpos (double_digits n)) with - (Zpos (double_digits n) + Zpos (double_digits n)). + unfold base. rewrite Pshiftl_nat_S, (Zpos_xO (_ << _)). + replace (2 * Zpos (w_digits << n)) with + (Zpos (w_digits << n) + Zpos (w_digits << n)) by ring. symmetry; apply Zpower_exp;intro;discriminate. - ring. Qed. Lemma double_wB_pos: @@ -309,7 +304,7 @@ Section DoubleBase. Proof. clear spec_w_0 spec_w_1 spec_w_Bm1 w_0 w_1 w_Bm1. intros n; elim n; clear n; auto. - unfold double_wB, double_digits; auto with zarith. + unfold double_wB, "<<"; auto with zarith. intros n H1; rewrite <- double_wB_wwB. apply Zle_trans with (wB * 1). rewrite Zmult_1_r; apply Zle_refl. |